"There are a lot of people in that bar..."

You can build things on planets, moons, gas giants and rocks but your mileage may vary - have a look at the guide in the space station database if you get stuck
Here's a video showing some gameplay (and some bugs) from a relatively recent version in case you can't play right now:
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Development progress is being tracked on TIG forums
Head on over to the downloads page to get your copy today!